If n(U) = 160, n(A′) = 63, n(B′) = 72, and n(A ∩ B) = 39, then what is n(A ∪ B)?
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Answer and explanation
Correct answer: 146
Use the complement relationship to find the sizes of A and B. Since n(A′) = n(U) − n(A), n(A) = 160 − 63 = 97. Similarly, n(B) = 160 − 72 = 88. Now apply the two-set union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 97 + 88 − 39 = 146. Thus the union contains 146 elements.
Frequently asked questions
What is the correct answer to this question?
146
Why is this the correct answer?
Use the complement relationship to find the sizes of A and B. Since n(A′) = n(U) − n(A), n(A) = 160 − 63 = 97. Similarly, n(B) = 160 − 72 = 88. Now apply the two-set union formula: n(A ∪ B) = n(A) + n(B) − n(A ∩ B) = 97 + 88 − 39 = 146. Thus the union contains 146 elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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